A Three-stage Cooperative Game Model for Water Resource Allocation Under Scarcity Using Bankruptcy Rules, Nash Bargaining Solution and TOPSIS

Abstract The global water security situation is deteriorating due to unequal distribution of water resources and changing climate, leading to increased conflicts in many regions. This article proposes and develops a three-stage collaborative water resource allocation model and applies this to the Indus River basin in Pakistan, where water resources are shared by four provinces (agents): Punjab, Sindh, Balochistan, and Khyber Pakhtunkhwa (KPK). The model uses bankruptcy rules, Nash bargaining theory, and TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) to allocate water resources. The model considers various factors, such as water risk and water satisfaction to achieve the best possible (most equitable and acceptable) outcome. Water allocation was conducted under three scenarios of ‘median’, ‘maximum’ and ‘low’ river flows. In the first stage of water allocation, the positive and negative ideal solutions were defined for all agents (in this case, provinces). These initial ideal solutions provided a baseline for the negotiation process. In the second stage, water allocation ratios of the four provinces Punjab, Sindh, Balochistan and KPK, using the Nash bargaining solution, under the median flows were 57.61%, 29.91%, 6.24% and 6.24%. In the third stage, water allocation ratios demonstrated the reduction in the allocation for those provinces facing high risks and having high satisfaction rates. The final allocations under the median flow conditions for the four provinces were 54.92%, 28.95%, 8.50% and 7.63%, respectively. The developed three-stage water allocation model considers the multi-dimensional attributes of water resources and is expected to support the cooperation of water agents, enabling collective bargaining and group negotiation and improving the acceptability and stability of allocations.